Old English hors, from Proto-Germanic *hursa- (cf. Old Norse hross, Old Frisian hors, Middle Dutch ors, Dutch ros, Old High German hros, German Roß "horse"), of unknown origin, connected by some with PIE root *kurs-, source of Latin currere "to run" (see current (adj.)).
The usual Indo-European word is represented by Old English eoh, from PIE *ekwo- "horse" (see equine). In many other languages, as in English, this root has been lost in favor of synonyms, probably via superstitious taboo on uttering the name of an animal so important in Indo-European religion.
Used since at least late 14c. of various devices or appliances which suggest a horse (e.g. sawhorse). To ride a horse that was foaled of an acorn (1670s) was through early 19c. a way to say "be hanged from the gallows." Slang for heroin is first attested 1950. Horse latitudes first attested 1777, the name of unknown origin, despite much speculation. Dead horse as a figure for "something that has ceased to be useful" is attested from 1630s.
The horse's mouth as a source of reliable information is from 1921, perhaps originally of racetrack tips, from the fact that a horse's age can be determined accurately by looking at its teeth. To swap horses while crossing the river (a bad idea) is from the American Civil War and appears to have been originally one of Abe Lincoln's stories. Horse and buggy meaning "old-fashioned" is recorded from 1926 slang, originally in reference to a "young lady out of date, with long hair." The proverbial gift horse was earlier given horse:
The modern form perhaps traces to Butler's "Hudibras" (1663), where the tight iambic tetrameter required a shorter phrase: